Answer:
Given the consumer is 18 to 24 years old, there is 37% probability that he uses a plastic card.
Step-by-step explanation:
This can be formulated as the following problem:
What is the probability of B happening, knowing that A has happened.
It can be calculated by the following formula
Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.
In this problem, we have:
What is the probability of the consumer using a plastic card, given that the consumer is 18 to 24 years old.
The problem states that the probability that a consumer uses a plastic card when making a purchase is .37, so
P(A/B) is the probability that the consumer being 18 to 24 years old, given that he uses a plastic card. The problem states that this probability is .19. So
P(A) is the probability that the consumer is 18 to 24 years old. There is a .81 probability that the consumer is more than 24 years old. So there is a .19 probability that he is 18 to 24 years old. So
The probability is
Given the consumer is 18 to 24 years old, there is 37% probability that he uses a plastic card.